The present invention relates to a closed-loop-type zero-system fiber optic gyro.
A wide-dynamic-range, low-drift fiber optic gyro that has been proposed in the past has an arrangement in which a phase modulator, formed as an optical modulator, is provided at one end of an optical fiber coil, a ramp voltage for phase modulation is applied to the phase modulator to provide a phase difference between two rays of light propagating through the optical fiber coil, a phase difference between two rays of light which propagate through the optical fiber coil and interfere with each other is detected from the output of a photodetector, and the polarity and frequency of the ramp voltage are controlled by the detected output so that the phase difference is 2 m.pi. rad (where m=0, .+-.1, .+-.2, . . . ), or zero (m=0), in general.
FIG. 1 illustrates an example of such a conventional closed-loop-type, zero-method fiber optic gyro of a linear phase ramp method which employs a ramp voltage for phase modulation. Light 12 from a light source 11 is applied via an optical coupler 13 and a polarizer 14 to an optical splitter/coupler 15, by which the light 12 is split into two rays of light 16a and 16b. The two rays of light 16a and 16b enter an optical fiber coil 17 at one and the other end 17a and 17b thereof, respectively, and propagate therethrough as left-handed and right-handed light 17a and 17b, thereafter being emitted therefrom as rays of light 18a and 18b. These rays of light 18a and 18b are supplied to the optical splitter/coupler 15, wherein they interfere with each other, and the resulting interference light 19 is applied via the polarizer 14 and the optical coupler 13 to a photodetector 21, whereby it is converted into an electric signal.
A phase modulator 22 is provided between the optical splitter/coupler 15 and the terminating end 17b of the optical fiber coil 17 and is supplied with a bias voltage Bi from a bias voltage generator 23. Consequently, the light 16b which enters the optical fiber coil 17 at the terminating end 17b and the light 18a which is applied from the terminating end 17b of the optical fiber coil 17 to the optical splitter/coupler 15 after having propagated through the coil 17 are phase-shifted relative to each other. Further, a phase modulator 24 is provided between the optical splitter/coupler 15 and the terminating end 17a of the optical fiber coil 17 and is supplied with a ramp voltage Rp from a ramp voltage generator 30. Consequently, the light 16a which enters the optical fiber coil 17 at its terminating end 17a and the light 18b which is applied from the terminating end 17a of the optical fiber coil 17 to the optical splitter/coupler 15 after having propagated through the coil 17 are phase-shifted. The output voltage Va of the photodetector 21 is provided to a synchronous detector 41 which forms a phase difference detect and control circuit 40 and in which it is synchronously detected by the bias voltage Bi from the bias voltage generator 23. As a result of this, a voltage Vb which corresponds to the phase difference .DELTA..phi. between the two rays of light 18a and 18b coupled together by the optical splitter/coupler 15 is detected by the synchronous detector 41 and is applied to a PID (Proportional plus Integral plus Derivative) filter 42. The output voltage of the PID filter 42, that is, the output voltage Vc of the phase difference detect and control circuit 40, is supplied to the ramp voltage generator 30, controlling the polarity and frequency of the ramp voltage Rp so that the phase difference .DELTA..phi. is reduced to zero.
The phase modulation in the phase modulator 22 by the biasing voltage Bi is intended to set the operation point of the fiber optic gyro so that the output voltage Vb of the synchronous detector 41 becomes proportional to the sine value of the phase difference .DELTA..phi. as follows. EQU Vb=Ksin.DELTA..phi. (1)
where K is a constant.
The phase difference .DELTA..phi. is expressed as the sum of a Sagnac phase difference .DELTA..phi..sub.s resulting from the application of angular velocity .OMEGA. to the optical fiber coil 17 and a phase difference .DELTA..phi..sub.p resulting from the application of the ramp voltage Rp to the phase modulator 24 as follows: EQU .DELTA..phi.=.DELTA..phi..sub.s +.DELTA..phi..sub.p ( 2)
As is well-known, the Sagnac phase difference .DELTA..phi..sub.s is expressed as follows: ##EQU1## where R is the radius of the optical fiber coil 17, L is the length of the optical fiber coil 17, .lambda. is the wavelength of light which propagates through the optical fiber coil 17 and C is the light velocity in a vacuum.
The ramp voltage Rp is a positive or negative sawtooth voltage as shown at the upper left or right-hand side in FIG. 2, and a maximum or minimum value of the ramp voltage corresponding to its peak value is selected such that the width of the phase shift .DELTA..phi. of light by the phase modulator 24 is 2k.pi. rad (where k=.+-.1, .+-.2, . . . ), in general and usually .+-.2.pi. rad.
For example, where the input angular velocity .OMEGA. is applied in the left-handed direction and the Sagnac phase difference .DELTA..phi..sub.s goes negative, the ramp voltage Rp is controlled to be a positive sawtooth voltage by the output voltage Vc of the phase difference detect and control circuit 40. In this instance, the phase shift .phi..sub.a, which is caused by the phase modulator 24 in the light 16a which enters the optical fiber coil 17 at its terminating end 17a, and the phase shift .phi..sub.b, which is caused by the phase modulator 24 in the light 18b which is applied to the optical splitter/coupler 15 from the terminating end 17a of the optical fiber coil 17 after propagating therethrough, bear such a relationship as indicated by the solid and broken lines at the lower left-hand side in FIG. 2, and the phase difference .DELTA..phi..sub.p which results from the application of the ramp voltage Rp to the phase modulator 24 goes positive. Where the input angular velocity .OMEGA. is applied in the right-handed direction and the Sagnac phase difference .DELTA..phi..sub.s goes positive, the ramp voltage Rp is controlled to be a negative sawtooth voltage by the output voltage Vc of the phase difference detect and control circuit 40. In this instance, the above-mentioned phase shifts .phi..sub.a and .phi..sub.b bear such a relationship as indicated by the solid and broken lines at the lower right-hand side in FIG. 2, and the above-mentioned phase difference .DELTA..phi..sub.p goes negative. In FIG. 2, .tau. is the time necessary for the propagation of light through the optical fiber coil 17.
Thus, letting the period and frequency of the ramp voltage Rp be represented by T and f, respectively, it follows that ##EQU2## as is evident from FIG. 2. Letting the refractive index of light in the optical fiber coil 17 be represented by n, the following relationship exists: ##EQU3## Hence, it follows that ##EQU4## Thus, by controlling the polarity and frequency f of the ramp voltage Rp so that the phase difference .DELTA..phi. expressed by Eq. (2) is reduced to zero, it follows, from Eqs. (6) and (3) and .DELTA..phi..sub.p =-.DELTA..phi..sub.s, that ##EQU5## The input angular velocity .OMEGA. is given as follows: ##EQU6## In the case where the input angular velocity .OMEGA. is applied in the left-handed direction, i.e. the negative direction and the ramp voltage Rp becomes a positive sawtooth voltage, however, k becomes a positive integer, and in the case where the input angular velocity .OMEGA. is applied in the right-handed direction, i.e. the positive direction and the ramp voltage Rp becomes a negative sawtooth voltage, k becomes a negative integer.
Thus, the direction and magnitude of the input angular velocity .OMEGA. can be measured from the polarity and frequency f of the ramp voltage Rp.
The phase modulator 24 usually has an optical waveguide formed as by diffusing titanium into an electro-optic crystal as of lithum niobate and a pair of electrodes across which voltage for modulation use is applied. The phase shift amount of light by such a phase modulator is proportional to the product .gamma. Vp of the electro-optic constant .gamma. of the electro-optic crystal and the applied voltage Vp. The electro-optic constant .gamma. is temperature dependent and has a temperature coefficient of about 500 ppm/.degree.C. though somewhat different according to the direction of cut of the electro-optic crystal. Accordingly, the phase shift amount of light in the phase modulator varies with temperature, even if the applied voltage Vp is constant.
In the prior art fiber optic gyro described above with respect to FIG. 1, a maximum or minimum value of the ramp voltage Rp which is applied to the phase modulator 24 from the ramp voltage generator 30 is fixed at such a value that a maximum phase shift of light in the phase modulator 24 by the ramp voltage Rp is 2k.pi. rad at a specified temperature of 15.degree. C., for example. Hence, if the temperature of the fiber optic gyro, and consequently the temperature of the phase modulator 24 deviates from the specified temperature owing to an environmental change, the electro-optic constant .gamma. of the electro-optic crystal forming the phase modulator 24 changes, resulting in the maximum phase shift deviating from 2 k.pi. rad. In consequence, the relationship between the input angular velocity .OMEGA. and the frequency f of the ramp voltage Rp, defined by Eq. (7) or (8) is lost, inducing a scale factor error in the output of the fiber optic gyro.
FIG. 3 shows the scale factor error in the conventional fiber optic gyro in the case where the peak value of the ramp voltage Rp was set so that the maximum phase shift would be .+-.2.pi. rad at 15.degree. C. When the temperature of the fiber optic gyro is 15.degree..+-.70.degree. C., that is, +85.degree. C. or -55.degree. C., the maximum phase shift deviates about 3.5% from .+-.2.pi. rad and the scale factor error is as large as approximately 0.06%. In the case where the ramp voltage Rp is a sawtooth voltage as mentioned above, however, a fly-back time exists in the sawtooth voltage, in practice; strictly speaking, Eq. (4) does not hold at a specified temperature and a scale factor error occurs in the output of the fiber optic gyro. FIG. 3 shows the case where the flyback time of the ramp voltage Rp was selected as short as 50 nanosec so that the scale factor error by the flyback time of the ramp voltage Rp would be negligibly small. Hence, the scale factor error shown in FIG. 3 is almost due entirely to the deviation of the maximum phase shift from .+-.2.pi. rad.